{"cells":[{"cell_type":"markdown","metadata":{"id":"B814D865AE2A4F47A3C9E6998FCFFCAB","jupyter":{},"mdEditEnable":false,"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"source":[" # Lecture 3: The Beta-Binomial Bayesian Model  \n"," \n"," ## Instructor: Dr. Hu Chuan-Peng  \n"]},{"cell_type":"markdown","metadata":{"id":"FE84E701C9D2489BA71EECC3FD573A0A","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":[" ## Part 1: Beta 先验"]},{"cell_type":"markdown","metadata":{"id":"11B4C87323064A9682BA3E25EB56201B","jupyter":{},"mdEditEnable":false,"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"source":["**“连任”**  \n","\n","纣王很想知道自己的支持率，于是他让姬发现在质子团中组织一次民意调查。\n","\n","![Image Name](https://cdn.kesci.com/upload/s141bvd2cb.PNG?imageView2/0/w/960/h/960)  \n","\n","在此前，类似的支持率调查已经进行过很多次，根据历史记录：\n","\n","- 纣王的支持率最低是35%，最高是55%，而平均支持率则在45%徘徊。"]},{"cell_type":"markdown","metadata":{"id":"68C5CB54CE994F6DAA3B576D2F31F44D","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 连续变量的先验模型"]},{"cell_type":"markdown","metadata":{"id":"4CEE16623157455782F90E965837F5E1","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**“支持率$\\pi$”**  \n","\n","> 在上一节课，我们将Kasparov的胜率定义为$\\pi$，$\\pi$的取值被简化为0.2，0.5，0.8，且每个胜率对应一个可能性取值(如，胜率为0.8的可能性为0.65)。这是离散先验的概率模型,(见图3.1左侧)。  \n","\n","对于任意一次民意调查，纣王的支持率都是未知的，$\\pi$可以取0-1之间的任何值。\n","\n","- 过去的选举情况为支持率提供了先验信息，因此我们可以为$\\pi$建立一个连续先验的概率模型(continuous prior probability)\n"]},{"cell_type":"code","execution_count":18,"id":"3be43bbb","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["       $\\pi$      $f(\\pi)$\n","0     0.0000  0.000000e+00\n","1     0.0001  8.312356e-27\n","2     0.0002  2.125836e-24\n","3     0.0003  5.442837e-23\n","4     0.0004  5.431262e-22\n","...      ...           ...\n","9995  0.9996  8.698716e-29\n","9996  0.9997  4.902475e-30\n","9997  0.9998  8.508448e-32\n","9998  0.9999  8.315682e-35\n","9999  1.0000  0.000000e+00\n","\n","[10000 rows x 2 columns]\n"]}],"source":["# 导入所需库\n","import pandas as pd\n","import seaborn as sns\n","import matplotlib.pyplot as plt\n","from scipy.stats import beta\n","import numpy as np\n","\n","# 创建离散先验分布数据\n","prior_disc = [0.2, 0.5, 0.8]         # 离散先验分布的取值\n","prior_dis_prob = [0.10, 0.25, 0.65]  # 对应的概率\n","prior_disc_data = pd.DataFrame({'$\\pi$': prior_disc, '$f(\\pi)$': prior_dis_prob})\n","\n","# 将'$\\pi$'列的数据类型转换为字符串，以便在图表中正确显示\n","prior_disc_data['$\\pi$'] = prior_disc_data['$\\pi$'].astype('str')\n","\n","# 定义计算 Beta 分布概率密度函数的函数\n","def calculate_beta_pdf(x):\n","    # 在这里示范了一个 Beta 分布的参数，你可以根据需要修改这些参数\n","    a = 9\n","    b = 11\n","    return beta.pdf(x, a, b)\n","\n","# 生成横坐标数据，创建连续先验分布数据\n","x = np.linspace(0, 1, 10000)         # 横坐标范围为 [0,1] 之间的 10000 个数\n","prior_conti_data = pd.DataFrame({'$\\pi$': x})\n","\n","# 计算每个横坐标点对应的 Beta 分布概率密度\n","prior_conti_data['$f(\\pi)$'] = prior_conti_data['$\\pi$'].apply(calculate_beta_pdf)\n","\n","# 打印生成的连续先验分布数据\n","print(prior_conti_data)\n"]},{"cell_type":"code","execution_count":21,"id":"f5f014c0","metadata":{},"outputs":[{"data":{"image/png":"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size 1500x400 with 2 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 创建一个包含两个子图的图表\n","f, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 4))\n","\n","# 在第一个子图中绘制离散先验分布的条形图\n","sns.barplot(data=prior_disc_data, x='$\\pi$', y='$f(\\pi)$', palette=\"deep\", ax=ax1)\n","\n","# 设置第一个子图的标题\n","ax1.set_title(\"discrete prior\")\n","\n","# 在第二个子图中绘制连续先验分布的线图\n","sns.lineplot(data=prior_conti_data, x=\"$\\pi$\", y=\"$f(\\pi)$\", color=\"black\", ax=ax2)\n","\n","# 设置第二个子图的标题\n","ax2.set_title(\"continuous prior\")\n","\n","# 移除图的上边框和右边框\n","sns.despine()\n","\n"]},{"cell_type":"markdown","metadata":{"id":"6B83C73E33A449648F6A872015AFAEF8","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### Beta 先验模型"]},{"cell_type":"markdown","metadata":{"id":"835FAD2C3ADB48C3A2F0FB7F01C9AB66","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**continuous probability models**  \n","\n","> 在上节课的例子中，$\\pi$是离散型随机变量$Y$，可以通过概率质量密度函数(probability mass function, pmf)来描述离散型随机变量在各特定取值上的概率，对所有$\\pi$的取值来说，$0\\leq \\pi \\leq 1$， 并且 $\\sum_{all\\,\\pmb{y}}f(\\pi) = 1$，$\\pi$取值的所有概率之和为1。\n","\n","当$\\pi$是一个连续的随机变量时，它服从于一个分布$f(\\pi)$, 又被称为概率密度函数(probability density function, pdf)  \n","\n","（1）pdf 与 pmf 有类似的性质：  \n","\n","- $f(\\pi) \\ge 0$  \n","- $\\int_\\pi f(\\pi)d\\pi = 1, f(\\pi)曲线下的面积之和为1$  \n","- 当$a \\le b$时，$P(a < \\pi < b) = \\int_a^b f(\\pi) d\\pi$  \n","\n","\n","![Image Name](https://cdn.kesci.com/upload/s0ywgsar31.jpg?imageView2/0/w/500/h/500)  \n","> source:https://www.zhihu.com/question/263467674/answer/1117758894"]},{"cell_type":"markdown","metadata":{"id":"3C68C6308A784FA58E5ED0AA360C07F6","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**为$\\pi$ 选择一个合适的分布-- Beta分布**  \n","\n","虽然我们潜意识里可能认为 $\\pi$ 服从正太分布 (如同之前的图表示那样)，然而，在统计世界中存在着许多分布。\n","\n","在这里，我们假设纣王的支持率$\\pi$服从Beta分布。  \n","\n","- 其中，Beta分布要求$\\pi$的取值范围满足[0,1]，\n","- 此外，Beta分布通过两个超参数(hyperparameters)，$\\alpha \\; (\\alpha>0)\\;和 \\beta\\;(\\beta>0)$ 调节分布的形态。 \n","\n","$$  \n","\\pi \\sim \\text{Beta}(\\alpha, \\beta).  \n","$$  \n"]},{"cell_type":"markdown","metadata":{"id":"3D563027DD1049A2ABB15D810A010511","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"subslide"},"tags":[]},"source":["**Beta分布的基础介绍**  \n","\n","**控制分布形状—— $\\alpha$和$\\beta$**  \n","\n","可视化网站：https://www.omnicalculator.com/statistics/beta-distribution#examples-of-beta-distribution-graphs  \n","\n","调整$\\alpha$和$\\beta$的大小，观察分布形状的变化  \n","\n","下图展示了不同$\\alpha$和$\\beta$下pdf形态的变化，实线代表均值，虚线代表众数  \n","\n","![imageName](https://www.bayesrulesbook.com/bookdown_files/figure-html/beta-tuning-1.png)  \n","-------------------------------\n","\n","**Beta分布的概率密度函数pdf**  \n","\n","$$  \n","f(\\pi) = \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\pi^{\\alpha-1} (1-\\pi)^{\\beta-1} \\;\\;  for\\; \\pi \\in [0,1] \\  \n","$$  \n","\n","*简单了解：*\n","\n","* *$\\Gamma$与阶乘有关*\n","\n","* *$\\Gamma(z) = \\int_0^\\infty x^{z-1}e^{-y}dx$ 且 $\\Gamma(z + 1) = z \\Gamma(z)$*  \n","\n","* *当z是正整数的时候，$\\Gamma(z)$ 可以被简化为$\\Gamma(z) = (z-1)!$*"]},{"cell_type":"markdown","metadata":{"id":"04B3A6DBB26741C4BA83E84B7022B6DB","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**调整Beta先验**  \n","\n","在这里我们选择$\\pi \\sim \\text{Beta}(45,55)$作为合理的先验模型\n","\n","* *关于为何$\\alpha=45, \\beta=55$，感兴趣的同学可自行查看课后bonus*\n","\n","带入公式，可以计算出先验$f(\\pi)$的pdf：  \n","\n","- pdf:  \n","$$\n","f(\\pi) = \\frac{\\Gamma(100)}{\\Gamma(45)\\Gamma(55)}\\pi^{44}(1-\\pi)^{54} \\;\\; \\text{ for } \\pi \\in [0,1]  .  \n","$$  \n"]},{"cell_type":"markdown","metadata":{"id":"143E2E0633DA452CB6834E053312A2D1","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["## Part 2 Binomial 与似然 "]},{"cell_type":"markdown","metadata":{"id":"EB36C20F7AD14CD2AC10EC3D06FF6E17","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### 二项数据模型&似然函数"]},{"cell_type":"markdown","metadata":{"id":"F7B81FF1058C44CDB14C8E69EDE1CD90","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["\n","确定先验之后，第二步，姬发要开始收集数据，构建似然函数  \n","\n","现在姬发在一个50人的质子群里发起了一场投票。\n","\n","假设其中支持纣王的人数为$Y$，我们知道，如果支持率$\\pi$越大，支持数$Y$也会更多。我们对选举结果做出如下假设：  \n","\n","1. 每个投票者的结果都是互不影响的(质子A的选择不会影响质子B的选择)  \n","\n","2. 任何一个质子支持纣王的可能性都为$\\pi$  \n","\n","\n","我们已经知道，在这两个前提下，支持数$Y$与支持率$\\pi$之间的关系符合二项分布：  \n","$$  \n","Y | \\pi \\sim \\text{Bin}(50, \\pi)  \n","$$  \n","\n","在不同的支持率下，出现特定支持数的可能性$f(y|\\pi)\\quad y \\in \\{0,1,2,...,50\\}$ 可以表示为：  \n","$$  \n","f(y|\\pi) = P(Y=y | \\pi) = \\binom{50}{y} \\pi^y (1-\\pi)^{50-y}  \n","$$  "]},{"cell_type":"markdown","id":"5d0f4a42","metadata":{},"source":["我们来进行一些具体的计算\n","\n","假设纣王的支持率只有0.1，在这个前提下，50人进行投票，投票结果$Y \\in ({1,2...50})$，而出现特定结果的概率可以表示为：\n","$$\n","f(Y=1|\\pi=0.1) = \\binom{50}{1} 0.1^1 (1-0.1)^{49}\n","$$\n","$$\n","f(Y=2|\\pi=0.1) = \\binom{50}{2} 0.1^2 (1-0.1)^{48}\n","$$\n","$$\n","...\n","$$\n","$$\n","f(Y=49|\\pi=0.1) = \\binom{50}{49} 0.1^{49} (1-0.1)^{1}\n","$$\n","$$\n","f(Y=50|\\pi=0.1) = \\binom{50}{50} 0.1^{50} (1-0.1)^{0}\n","$$\n","\n","我们可以把这50个概率值画出来"]},{"cell_type":"code","execution_count":14,"id":"454dfcec","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 导入必要的库\n","from scipy.stats import binom\n","import numpy as np\n","import pandas as pd\n","import seaborn as sns\n","import matplotlib.pyplot as plt\n","\n","# 设置二项分布的参数\n","n = 50  # 总试验次数\n","p = 0.1  # 单次试验成功的概率\n","\n","# 创建一个包含从0到50的整数的数组\n","k = np.arange(0, 51)\n","\n","# 创建一个包含 'Y' 列的DataFrame\n","Y_data = pd.DataFrame({'Y': k})\n","\n","# 计算每个 'Y' 对应的概率，并将结果存储在 'prob' 列中\n","Y_data['prob'] = Y_data['Y'].apply(lambda x: binom.pmf(x, n, p))\n","\n","# 创建一个柱状图，表示概率分布\n","dist_pi_01 = sns.barplot(data=Y_data, x='Y', y='prob', color=\"grey\")\n","\n","# 设置图的标题\n","dist_pi_01.set_title(\"Beta(50,0.1)\")\n","\n","# 设置y轴标签\n","dist_pi_01.set(\n","    ylabel=\"$f(y|\\\\pi=0.1)$\",       # 使用LaTeX标记设置y轴标签\n","    xticks=[0, 10, 20, 30, 40, 50]  # 设置x轴刻度\n",")\n","\n","# 移除图的上边框和右边框\n","sns.despine()"]},{"cell_type":"markdown","id":"b6506da1","metadata":{},"source":["**不同支持率下的投票数情况分布**\n","\n","可以看到，当支持率$\\pi$很低时，支持数$Y$集中在0-10之间。这很符合我们的直觉\n","\n","同样的，我们可以查看不同支持率$\\pi$下，支持数$Y$的分布情况\n","（注：这里只展示了当支持率$\\pi$ =0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 九种情况下的分布图，但是记住$\\pi$的取值其实是有无穷多个的）"]},{"cell_type":"code","execution_count":15,"id":"39ec745b","metadata":{},"outputs":[{"data":{"text/plain":["<seaborn.axisgrid.FacetGrid at 0x1c0216d2590>"]},"execution_count":15,"metadata":{},"output_type":"execute_result"},{"data":{"image/png":"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","text/plain":["<Figure size 900x900 with 9 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 导入必要的库\n","import numpy as np\n","import pandas as pd\n","from scipy.stats import binom\n","import seaborn as sns\n","import matplotlib.pyplot as plt\n","\n","# 设置二项分布的参数\n","n = 50  # 总试验次数\n","p_values = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]  # 不同的 p 值列表\n","k = np.arange(0, 51)                                      # 创建一个包含从0到50的整数的数组\n","\n","# 创建一个包含 'Y' 列的 DataFrame\n","dist_all_pi = pd.DataFrame({'Y': k})\n","\n","# 计算每个 'Y' 对应的概率，并将结果存储在相应列中\n","for p in p_values:\n","    column_name = f'{p}'\n","    dist_all_pi[column_name] = dist_all_pi['Y'].apply(lambda x: binom.pmf(x, n, p))\n","\n","# 使用 stack() 和 reset_index() 转换数据为长格式\n","melted_data = dist_all_pi.set_index('Y').stack().reset_index()\n","melted_data.columns = ['Y', 'p', 'prob']\n","\n","# 创建一个 FacetGrid 对象，用于绘制子图\n","plot_all_pi = sns.FacetGrid(melted_data, col='p', col_wrap=3)\n","\n","# 使用柱状图绘制概率分布\n","plot_all_pi.map(sns.barplot, 'Y', 'prob', color=\"grey\", order=None)\n","\n","# 设置 x 和 y 轴的刻度和范围\n","plot_all_pi.set(xticks=[0, 10, 20, 30, 40, 50],\n","                yticks=[0.00, 0.05, 0.10, 0.15],\n","                ylim=(0, 0.20))\n","\n","# 设置 y 轴标签\n","plot_all_pi.set_ylabels(\"$f(y|\\\\pi)$\")\n","\n","# 设置子图的标题模板\n","plot_all_pi.set_titles(col_template=\"Bin(50,{col_name})\")\n","\n","# 显示x=30的点\n","# for ax in g.axes.flat:\n","#     ax.scatter(x=30, y=0, color='red', marker='o', s=60)\n","# g.show()\n"]},{"cell_type":"markdown","id":"56b012a2","metadata":{"slideshow":{"slide_type":"subslide"}},"source":["支持率高时，投票数高的情况更可能出现；支持率低时，更可能出现的是投票数低的情况，这很符合我们的直觉。  \n","\n","我们可以关注各个支持率下，投票数$Y=30$发生的概率（下图黑点）\n","\n","![image](https://www.bayesrulesbook.com/bookdown_files/figure-html/binoms-3-1.png)\n","\n","\n"]},{"cell_type":"markdown","id":"5cb6b929","metadata":{},"source":["**$Y=30$ 的似然函数**\n","\n","把不同支持率下，$Y=30$发生的可能性用公式表示出来，写成：\n","\n","$$\n","f(Y=30|\\pi=0.1) = \\binom{50}{30} 0.1^{30} (1-0.1)^{20}\n","$$\n","$$\n","f(Y=30|\\pi=0.2) = \\binom{50}{30} 0.2^{30} (1-0.2)^{20}\n","$$\n","$$\n","...\n","$$\n","$$\n","f(Y=30|\\pi=0.8) = \\binom{50}{30} 0.8^{30} (1-0.8)^{20}\n","$$\n","$$\n","f(Y=30|\\pi=0.9) = \\binom{50}{30} 0.9^{30} (1-0.9)^{20}\n","$$\n","\n","> 注意和先前的 “特定$\\pi$下，不同事件发生的概率” 做一个区分\n","\n","将不同支持率$\\pi \\in (0~1)$下，$Y=30$发生的相对可能性组合在一起，就构成了一个似然函数:\n","\n","$$  \n","L(\\pi | y=30) = \\binom{50}{30} \\pi^{30} (1-\\pi)^{20} \\; \\;  for \\; \\pi \\in [0,1]  .  \n","$$  \n","\n","------------------------\n","\n","把上图中，黑点们代表的概率都提出来，组合到一起，就构成了$Y=30$下的概率密度函数\n","<center>  \n","\n","![image](https://www.bayesrulesbook.com/bookdown_files/figure-html/likelihood-election-ch3-1.png)  \n","\n","</center>  \n","\n","从两幅图中，我们都可以发现，当$\\pi=0.6$时，$L(\\pi|y=30)$ 取到最大值。也就是说投票数为30这个情况最可能在当$\\pi = 0.6$时出现  "]},{"cell_type":"markdown","metadata":{"id":"16AFF80DBE9A441F9A2E37084A6D52C0","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["### Beta 后验模型"]},{"cell_type":"markdown","metadata":{"id":"523199278392457083D6EBDBAAC69CEC","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["当我们有了先验与似然两种信息，可以尝试进行推断后验：  \n","\n","$$  \n","\\begin{align*} \n","Y | \\pi & \\sim \\text{Bin}(50, \\pi)  \\\\  \n","    \\pi & \\sim \\text{Beta}(45, 55). \\\\  \n","\\end{align*}    \n","$$  \n","\n","<center>  \n","\n","![imageName](https://www.bayesrulesbook.com/bookdown_files/figure-html/like-election-ch3-1.png)  \n","\n","</center>  \n","\n","* 注意，在这里，为了方便在视觉上对比先验和似然，似然函数被缩放为相加和为1"]},{"cell_type":"markdown","metadata":{"id":"903D48A99A684AC08D2437F0534B8CD1","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**思考🧐**  \n","\n","哪一张图正确反映了$\\pi$的后验模型？  \n","\n","\n","![imageName](https://www.bayesrulesbook.com/bookdown_files/figure-html/unnamed-chunk-105-1.png)"]},{"cell_type":"markdown","metadata":{"id":"1B51D2441D1443E79E6250BB7A664EEE","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["我们可以画出后验分布图："]},{"cell_type":"code","execution_count":81,"metadata":{"collapsed":false,"id":"9DDED6FDE90A44818772930A7E2C79CB","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","scrolled":false,"slideshow":{"slide_type":"subslide"},"tags":[],"trusted":true},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 导入统计建模工具包 scipy.stats 为 st\n","import scipy.stats as st \n","\n","# 设置 x 轴范围 [0,1]\n","x = np.linspace(0,1,10000)\n","# 设置 Beta 分布参数\n","a,b = 45,55\n","# 形成先验分布 \n","prior = beta.pdf(x,a,b)/np.sum(beta.pdf(x,a,b))\n","\n","# 形成似然\n","k = 30     # k 代表支持数\n","n = 50     # n 代表总投票数\n","likelihood = st.binom.pmf(k,n,x)\n","\n","# 计算后验\n","unnorm_posterior = prior * likelihood                  # 计算分子\n","posterior = unnorm_posterior/np.sum(unnorm_posterior)  # 结合分母进行计算\n","likelihood = likelihood /np.sum(likelihood)            # 为了方便可视化，对似然进行类似后验的归一化操作 \n","\n","# 绘图\n","plt.plot(x,posterior, color=\"#009e74\", alpha=0.5, label=\"posterior\")\n","plt.plot(x,likelihood, color=\"#0071b2\", alpha=0.5, label=\"likelihood\")\n","plt.plot(x,prior, color=\"#f0e442\", alpha=0.5, label=\"prior\")\n","plt.legend()\n","plt.xlabel(\"Michelle's support ratio $\\pi$\")\n","plt.fill_between(x, prior, color=\"#f0e442\", alpha=0.5)\n","plt.fill_between(x, likelihood, color=\"#0071b2\", alpha=0.5)\n","plt.fill_between(x, posterior, color=\"#009e74\", alpha=0.5)\n","sns.despine()"]},{"cell_type":"markdown","metadata":{"id":"2CFC17D91DAB49F1AF5658EAA88F8A23","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"subslide"},"tags":[]},"source":["**正式计算**  \n","\n","$$  \n","f(\\pi | y = 30) = \\frac{f(\\pi)L(\\pi|y = 30)}{f(y = 30)}.  \n","$$  \n","\n","和之前一样，分母$f(y = 30)$是一个常数，在计算中可以将其忽略  \n","\n","$$  \n","\n","f(\\pi | y = 30) \\propto f(\\pi) L(\\pi | y=30)  \\\\  \n","=\\frac{\\Gamma(100)}{\\Gamma(45)\\Gamma(55)}\\pi^{44}(1-\\pi)^{54} \\cdot \\binom{50}{30} \\pi^{30} (1-\\pi)^{20}\\\\  \n","= [\\frac{\\Gamma(100)}{\\Gamma(45)\\Gamma(55)}\\binom{50}{30}]  \\cdot \\pi^{74} (1-\\pi)^{74}  \\\\  \n","\\propto \\pi^{74} (1-\\pi)^{74} \\\\  \n","\\\\  \n","[\\;] 中的也是可以忽略的常数项 \\\\  \n","\n","$$"]},{"cell_type":"markdown","metadata":{"id":"44D761E362B641ADB137B93E2B1344D4","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"subslide"},"tags":[]},"source":["整理一下可知，后验分布可以表示为：  \n","$$  \n","f(\\pi | y=30) = c \\pi^{74} (1-\\pi)^{74} \\propto \\pi^{74} (1-\\pi)^{74}  \n","$$  \n","\n","\n","根据这个公式，我们发现 $f(\\pi | y=30)$ 和 $Beta(75,75)$ 有着相似的形状  \n","\n","$$  \n","Beta(75,75) = \\frac{\\Gamma(150)}{\\Gamma(75)\\Gamma(75)}\\pi^{74} (1-\\pi)^{74}  \n","$$  \n","\n","实际上，在这里后验分布也确实是Beta分布：  \n","\n","$$  \n","\\pi | (Y = 30) \\sim \\text{Beta}(75,75)  \n","$$"]},{"cell_type":"markdown","metadata":{"id":"80BC532C765048CBA4C3750B9C59CA36","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","runtime":{"execution_status":null,"status":"default"},"scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[]},"source":["**对后验模型进行总结**  \n","\n","在结合先验和似然之后，我们对支持率$\\pi$的认识发生了更新。  \n","\n","需要注意的是：后验模型仍然是一个$Beta$分布，和先验模型一样。  \n","\n","$$  \n","\\pi | (Y = 30) \\sim \\text{Beta}(75,75)  \n","$$  \n","\n","\n","$$  \n","f(\\pi | y = 30) = \\frac{\\Gamma(150)}{\\Gamma(75)\\Gamma(75)}\\pi^{74} (1-\\pi)^{74}  \n","$$  \n","\n","所以我们也可以对二者进行对比，下表进行了这一总结，可以发现，在新的数据产生之后：  \n","\n","例如：  \n","\n","- 对支持率的期望值从0.45增加为0.50；  \n","\n","- 模型的标准差从0.0495减少为0.0407；  \n","\t\n","|    |prior  |posterior  \n","|----|-----|----|  \n","|$\\alpha$   |45  |75 |  \n","|$\\beta$   |75  |75 |  \n","|mean   |0.45  |0.50 |  \n","|mode  |0.449  |0.500 |  \n","|var   |0.00245  |0.001656 |  \n","|sd   |0.04950  |0.04069 |  \n"]},{"cell_type":"markdown","id":"fecd02c4","metadata":{},"source":["**思考🧐**\n","\n","- 先验分布的形态是否决定了后验分布的形态？(还记得之前关于正态分布和Beta分布的例子吗)\n","- 先验分布和后验分布是否必然一致？"]},{"cell_type":"markdown","id":"a98a8b79","metadata":{},"source":["### Part 3: Beta-Binomial model and simulation"]},{"cell_type":"markdown","id":"2b83d62b","metadata":{"collapsed":false,"id":"4DE14997A6F345B19CA29919ACA9EB88","jupyter":{},"notebookId":"6502c6f1518d0a92c0c3c0ca","scrolled":false,"slideshow":{"slide_type":"slide"},"tags":[],"trusted":true},"source":["**Beta-Binomial model 的一般数学形式**\n","\n","在前一节中，我们为纣王的支持率$\\pi$建立了基本的Beta-Binomial模型。\n","\n","- 我们假设了一个特定的Beta(45,55)先验分布和特定的民意调查结果（支持者： Y = 30，总人数： n = 50）。\n","- 这只是Beta-Binomial模型的一个特例。 实际上 Beta 模型可以适用于任何参数范围($\\pi$)在[0,1]的场景。\n","- 例如，$\\pi$可以表示硬币为正面的倾向，或者表示使用社交媒体的成年人比例。\n","\n","$$\n","\\begin{split}\n","Y | \\pi & \\sim \\text{Bin}(n, \\pi) \\\\\n","\\pi & \\sim \\text{Beta}(\\alpha, \\beta). \\\\\n","\\end{split}\n","$$\n","\n","\n","无论是哪种情况，在观察到 n 次时间中有 Y = y次目标事件后，$\\pi$的后验分布可以用Beta模型来描述，反映了先验（通过α和β）和数据（通过y和n）的影响：\n","\n","$$\n","\\begin{equation}\n","\\pi | (Y = y) \\sim \\text{Beta}(\\alpha + y, \\beta + n - y)  .\n","\\tag{3.10}\n","\\end{equation}\n","$$\n","\n","\n","需要注意的是，后验与先验是相同的概率模型，只是参数不同\n","\n","- 在这个例子中，Beta(α, β)模型是对应数据模型的 $\\text{Bin}(n, \\pi)$ 的**共轭先验 (conjugate prior)**。\n","- 如果 f($\\pi$)是L($\\pi$∣y)的共轭先验，后验f($\\pi$∣y) ∝ f($\\pi$)L($\\pi$∣y)与先验来自相同的模型族。\n","- 我们将在第五次课详细介绍共轭先验的相关知识。\n"]},{"cell_type":"markdown","id":"fd28b642","metadata":{},"source":["**代码实现**\n","\n","让我们模拟纣王的支持率π的后验模型。\n","\n","- 首先，我们从Beta(45,55)先验中模拟10,000个π值，\n","- 然后, 使用从每个π值中模拟Bin(50,π)的潜在调查结果Y：\n","\n","模拟结果：10,000对π和y值\n"]},{"cell_type":"code","execution_count":1,"id":"0345259f","metadata":{"slideshow":{"slide_type":"fragment"}},"outputs":[{"data":{"text/html":["<div>\n","<style scoped>\n","    .dataframe tbody tr th:only-of-type {\n","        vertical-align: middle;\n","    }\n","\n","    .dataframe tbody tr th {\n","        vertical-align: top;\n","    }\n","\n","    .dataframe thead th {\n","        text-align: right;\n","    }\n","</style>\n","<table border=\"1\" class=\"dataframe\">\n","  <thead>\n","    <tr style=\"text-align: right;\">\n","      <th></th>\n","      <th>pi</th>\n","      <th>y</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>0.479492</td>\n","      <td>28</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>0.385205</td>\n","      <td>16</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>0.412269</td>\n","      <td>19</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>0.458158</td>\n","      <td>20</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>0.397845</td>\n","      <td>24</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>"],"text/plain":["         pi   y\n","0  0.479492  28\n","1  0.385205  16\n","2  0.412269  19\n","3  0.458158  20\n","4  0.397845  24"]},"execution_count":1,"metadata":{},"output_type":"execute_result"}],"source":["# 导入数据加载和处理包：pandas\n","import pandas as pd\n","# 导入数字和向量处理包：numpy\n","import numpy as np\n","# 导入基本绘图工具：matplotlib\n","import matplotlib.pyplot as plt\n","\n","# 设置随机种子，以便后续可以重复结果\n","np.random.seed(84735)\n","# 模拟 10000 次数据\n","king_sim = pd.DataFrame({'pi': np.random.beta(45, 55, size=10000)})  # 从Beta(45,55)先验中模拟10,000个π值\n","king_sim['y'] = np.random.binomial(n=50, p=king_sim['pi'])       # 从每个π值中模拟Bin(50,π)的潜在调查结果Y\n","\n","# 显示部分数据\n","king_sim.head()"]},{"cell_type":"markdown","id":"934e20a6","metadata":{},"source":["通过散点图观察以上数据的关系:\n","- 黑色点表示支持数Y!=30的部分。\n","- 蓝色点表示支持数Y=30的部分。"]},{"cell_type":"code","execution_count":18,"id":"400fd9d8","metadata":{"slideshow":{"slide_type":"fragment"}},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 绘制散点图：非调查结果 (Y!=30)部分，用黑色表示\n","plt.scatter(king_sim['pi'][king_sim['y']!=30], \n","            king_sim['y'][king_sim['y']!=30], \n","            c='black', s = 3,\n","            label='FALSE')\n","# 绘制散点图：调查结果 (Y=30)部分，用蓝色表示\n","plt.scatter(king_sim['pi'][king_sim['y']==30],\n","            king_sim['y'][king_sim['y']==30],\n","            c='b', s = 20, \n","            label='TRUE')\n","\n","# 显示图片\n","plt.legend(title = \"y==30\")\n","plt.xlabel('$\\pi$')\n","plt.ylabel('Y')\n","plt.show()"]},{"cell_type":"markdown","id":"8e978b23","metadata":{},"source":["当我们仅关注与我们的Y = 30调查结果匹配的对时，剩下的π值的很好地逼近了后验模型Beta(75,75)："]},{"cell_type":"code","execution_count":26,"id":"cb5c43a6","metadata":{"slideshow":{"slide_type":"fragment"}},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 500x500 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 导入高级绘图工具 seaborn 为 sns\n","import seaborn as sns\n","\n","king_posterior = king_sim[king_sim['y'] == 30]\n","\n","# 绘制分布图：概率密度+柱状图\n","sns.displot(king_posterior['pi'], kde=True)\n","plt.xlabel('$\\pi$')\n","plt.ylabel('Density')\n","plt.show()"]},{"cell_type":"markdown","id":"2814dad0","metadata":{},"source":["同时绘制出先验、似然和后验。"]},{"cell_type":"code","execution_count":82,"id":"514154ff","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["<Figure size 640x480 with 1 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["# 导入统计建模工具包 scipy.stats 为 st\n","import scipy.stats as st \n","\n","# 设置 x 轴范围 [0,1]\n","x = np.linspace(0,1,10000)\n","# 设置 Beta 分布参数\n","a,b = 45,55\n","# 形成先验分布 \n","prior = beta.pdf(x,a,b)/np.sum(beta.pdf(x,a,b))\n","\n","# 形成似然\n","k = 30                  # k 代表支持数\n","n = 50                  # n 代表总投票数\n","likelihood = st.binom.pmf(k,n,x)\n","\n","# 计算后验\n","unnorm_posterior = prior * likelihood                  # 计算分子\n","posterior = unnorm_posterior/np.sum(unnorm_posterior)  # 结合分母进行计算\n","likelihood = likelihood /np.sum(likelihood)            # 为了方便可视化，对似然进行类似后验的归一化操作 \n","\n","# 绘图\n","plt.plot(x,posterior, color=\"#009e74\", alpha=0.5, label=\"posterior\")\n","plt.plot(x,likelihood, color=\"#0071b2\", alpha=0.5, label=\"likelihood\")\n","plt.plot(x,prior, color=\"#f0e442\", alpha=0.5, label=\"prior\")\n","plt.legend()\n","plt.xlabel(\"king's support ratio $\\pi$\")\n","plt.fill_between(x, prior, color=\"#f0e442\", alpha=0.5)\n","plt.fill_between(x, likelihood, color=\"#0071b2\", alpha=0.5)\n","plt.fill_between(x, posterior, color=\"#009e74\", alpha=0.5)\n","plt.xlim([0,1])\n","plt.show()"]},{"cell_type":"markdown","id":"9d465c3d","metadata":{},"source":["我们还可以使用模拟样本近似后验特征，例如Michelle支持率的均值和标准差。\n","\n","- 结果与上面计算的理论值非常相似，E(π∣Y = 30) = 0.5和SD(π∣Y = 30) = 0.0407：\n","- 在解释这些模拟结果时，“近似”是一个关键词。由于我们10,000次模拟中只有219次与观测到的Y = 30数据匹配，通过将原始模拟次数从10,000增加到50,000，可以改善这个近似值："]},{"cell_type":"code","execution_count":29,"id":"abb0895c","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["近似值： 均值， 0.5024772340319912 。标准差， 0.0394983348061003\n"]}],"source":["print(\n","  \"近似值：\", \n","  \"均值，\",\n","  king_posterior['pi'].mean(), \n","  \"。标准差，\",\n","  king_posterior['pi'].std()\n",")"]},{"cell_type":"code","execution_count":34,"id":"ae5ea301","metadata":{},"outputs":[{"name":"stdout","output_type":"stream","text":["10,000次模拟中, 219次与观测到的Y = 30数据匹配\n","50,000次模拟中, 1045次与观测到的Y = 30数据匹配\n"]}],"source":["print(f\"10,000次模拟中, {king_posterior.shape[0]}次与观测到的Y = 30数据匹配\")\n","\n","# 模拟新的数据\n","size = 50000 # 不同于之前的 10000\n","king_sim2 = pd.DataFrame({'pi': np.random.beta(45, 55, size=size)})\n","king_sim2['y'] = np.random.binomial(n=50, p=king_sim2['pi'])\n","king_posterior2 = king_sim2[king_sim2['y'] == 30]\n","print(f\"50,000次模拟中, {king_posterior2.shape[0]}次与观测到的Y = 30数据匹配\")"]},{"cell_type":"markdown","id":"2f093a29","metadata":{},"source":["### 🎈总结 \n","\n","在第3章中，我们学习了构建了Beta-binomial二项式模型,用于描述取值范围在0到1之间的比例π:\n","\n","$$\n","\\begin{split}\n","Y | \\pi &\\sim \\text{Bin}(n, \\pi) \\\\  \n","\\pi &\\sim \\text{Beta}(\\alpha, \\beta)\n","\\end{split}\n","\\Rightarrow \\pi | (Y = y) \\sim \\text{Beta}(\\alpha + y, \\beta + n - y).\n","$$\n","\n","这个模型反映了贝叶斯分析的四个通用要素:\n","\n","1. 先验模型 Beta先验模型可以通过调节参数来反映不同的π值在[0,1]范围内的相对先验可能性。\n","\n","$$\n","f(\\pi) = \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)}\\pi^{\\alpha - 1}(1-\\pi)^{\\beta - 1}.\n","$$\n","\n","2. 数据模型 为了学习π,我们收集数据Y,即n次独立试验中成功的次数,其中每次试验成功的概率为π。Y对π的依赖关系由二项分布Bin(n, π)总结。\n","\n","3. 似然函数 在观测到数据Y=y,其中y∈{0,1,...,n}后,π的似然函数通过将y代入二项式概率质量函数而获得,它提供了一种机制来比较不同π与数据的兼容性:\n","\n","$$\n","L(\\pi|y) = \\binom{n}{y}\\pi^y(1-\\pi)^{n-y} \\text{ for } \\pi \\in [0,1].\n","$$\n","\n","4. 后验模型 通过贝叶斯规则,共轭的Beta先验和二项式数据模型结合产生π的Beta后验模型。更新的Beta后验参数(α + y,β + n - y)反映了先验的影响(通过α和β)和观测数据的影响(通过y和n)。\n","\n","$$\n","f(\\pi|y) \\propto f(\\pi)L(\\pi|y) \\propto \\pi^{(\\alpha+y)-1}(1-\\pi)^{(\\beta+n-y)-1}.\n","$$"]},{"cell_type":"markdown","id":"d5df99b2","metadata":{},"source":["**🥋练习**\n","\n","- 假设虚假新闻出现的概率为 0.4 ($\\pi$ = 0.4)， 请自行选择一个合适的 Beta 分布，模拟10000个$\\pi$值。\n","- 请根据 $\\pi$ 模拟相应的数据 Y (虚假新闻的数量)，假设总的新闻数量 n = 100。\n","- 绘制先验分布和后验分布的图像。\n","\n","\n","其中设计的python基础操作请参考：\n","\n","![Image Name](https://cdn.kesci.com/upload/s0vfx2ld9v.png?imageView2/0/w/1280/h/1280)"]},{"cell_type":"markdown","id":"7e576cb1","metadata":{},"source":["### Bonus 1：Beta(45,55)这个先验是怎么选取的?"]},{"cell_type":"markdown","id":"854ae166","metadata":{},"source":["**Beta分布的集中趋势量数**\n","\n","在回答这个问题之前，我们先来了解一下**Beta分布的集中趋势量数**  \n","\n","需要注意的是，虽然我们可能比较熟悉计算正态分布的均值、众数和标准差；但 Beta 分布的相关统计量的计算有所不同：\n","\n","![Image Name](https://cdn.kesci.com/upload/s0ywp66o5v.png?imageView2/0/w/500/h/500)  \n",">source:https://en.wikipedia.org/wiki/Probability_density_function\n","\n","**1. 平均数(mean)**  \n","\n","- $\\pi$的平均取值  \n","$$  \n","E(\\pi)  = \\frac{\\alpha}{\\alpha + \\beta}  \n","$$  \n","$$  \n","E(\\pi) = \\int \\pi \\cdot f(\\pi)d\\pi.  \n","$$  \n","\n","**2. 众数(mode)**  \n","\n","- $\\pi$最可能的取值。即，在$\\pi$下，$f(\\pi)$能取到最大值。  \n","\n","$$  \n","\\text{Mode}(\\pi)  = \\frac{\\alpha - 1}{\\alpha + \\beta - 2} \\;\\;\\; \\text{ when } \\; \\alpha, \\beta > 1.  \n","$$  \n","$$  \n","\\text{Mode}(\\pi) = \\text{argmax}_\\pi f(\\pi).  \n","$$  \n","**3. 方差(variance)**  \n","\n","- $\\pi$取值的可变性(variability)  \n","$$  \n","\\text{Var}(\\pi) = E((\\pi - E(\\pi))^2) = \\int (\\pi - E(\\pi))^2 \\cdot f(\\pi) d\\pi.  \n","$$  \n","\n","$$  \n","\\text{Var}(\\pi) = \\frac{\\alpha \\beta}{(\\alpha + \\beta)^2(\\alpha + \\beta + 1)} .  \n","$$  \n","\n","**4. 标准差(standard deviation)**  \n","$$  \n","\\text{SD}(\\pi) := \\sqrt{\\text{Var}(\\pi)} .  \n","$$"]},{"cell_type":"markdown","id":"d81a3212","metadata":{},"source":["**调整Beta先验**  \n","\n","我们已经知道，Michelle的平均支持率为45%。我们可以根据这一点来计算beta分布的$\\alpha$和$\\beta$。  \n","$$  \n","E(\\pi) = \\alpha/(\\alpha + \\beta) \\approx 0.45  \n","$$  \n","重新整理过后：  \n","$$  \n","\\alpha \\approx \\frac{9}{11} \\beta  \n","$$  \n","一个合适的分布中，$\\alpha$和$\\beta$需要满足的条件如上，我们可以选择 *Beta(9,11), Beta(27,33), Beta(45,55)*，我们可以通过以下代码来画出这些分布的形状"]},{"cell_type":"code","execution_count":null,"id":"bc0e04c4","metadata":{},"outputs":[{"data":{"text/plain":["Text(0.5, 1.0, 'beta(45,55)')"]},"metadata":{},"output_type":"display_data"},{"data":{"text/html":["<img src=\"https://cdn.kesci.com/upload/rt/FB5E10D3817F4BDA8BE077508EC6503E/s0ywsbopz8.png\">"],"text/plain":["<Figure size 1080x360 with 3 Axes>"]},"metadata":{},"output_type":"display_data"}],"source":["import numpy as np\n","from scipy.stats import beta\n","import matplotlib.pyplot as plt\n","\n","x = np.linspace(0,1,10000)\n","y1 = beta.pdf(x,9,11)\n","y2 = beta.pdf(x,27,33)\n","y3 = beta.pdf(x,45,55)\n","\n","fig, axes = plt.subplots(1, 3, figsize=(15, 5))\n","axes[0].plot(x,y1)\n","axes[0].set_title(\"Beta(9,11)\")\n","axes[1].plot(x,y2)\n","axes[1].set_title(\"Beta(27,33)\")\n","axes[2].plot(x,y3)\n","axes[2].set_title(\"Beta(45,55)\")"]},{"cell_type":"markdown","id":"040ce47f","metadata":{},"source":["如图所示，我们选择$\\pi \\sim \\text{Beta}(45,55)$作为合理的先验模型  \n","\n","带入公式，可以计算出$先验f(\\pi)$的pdf、平均数、众数、方差和标准差：  \n","\n","- pdf:  \n","$$  \n","f(\\pi) = \\frac{\\Gamma(100)}{\\Gamma(45)\\Gamma(55)}\\pi^{44}(1-\\pi)^{54} \\;\\; \\text{ for } \\pi \\in [0,1]  .  \n","$$  \n","\n","- 平均数:  \n","$$  \n","E(\\pi) = \\frac{45}{45 + 55} = 0.4500  \n","$$  \n","\n","- 众数:  \n","$$  \n","\\text{Mode}(\\pi) = \\frac{45 - 1}{45 + 55 - 2} = 0.4490  \n","$$  \n","\n","- 方差:  \n","$$  \n","\\text{Var}(\\pi)  = \\frac{45 \\cdot 55}{(45 + 55)^2(45 + 55 + 1)} = 0.0025  \n","$$  \n","\n","- 标准差：  \n","$$  \n","\\text{SD}(\\pi)   = \\sqrt{0.0025} = 0.05.  \n","$$  \n","\n","\n","\n"]},{"cell_type":"markdown","id":"e6f66962","metadata":{},"source":["### Bonus2 Beta-Binomial 模型生成的后验仍是Beta分布"]},{"cell_type":"markdown","id":"f05af856","metadata":{},"source":["**公式推导**\n","\n","对于 $\\pi$ 的后验模型为 $Beta(α + y, β + n − y)$ 的推导过程 (其中，支持者为y，总人数为n)。\n","\n","1. 首先写出先验的公式\n","\n","$$\n","\\begin{equation}\n","f(\\pi) = \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)}\\pi^{\\alpha - 1}(1-\\pi)^{\\beta - 1} \n","\\;\\; \\text{ and } \\;\\; \n","L(\\pi|y) = \\left(\\!\\!\\begin{array}{c} n \\\\ y\\end{array}\\!\\!\\right) \\pi^{y} (1-\\pi)^{n-y}  .\n","\\tag{3.12}\n","\\end{equation}\n","$$\n","\n","2. 结合先验和似然函数 (暂时忽略分母)，后验概率密度函数可以由贝叶斯定理得到：\n","\n","$$\n","\\begin{split}\n","f(\\pi | y)\n","& \\propto f(\\pi)L(\\pi|y) \\\\\n","& = \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)}\\pi^{\\alpha - 1}(1-\\pi)^{\\beta - 1}  \\cdot \\left(\\!\\begin{array}{c} n \\\\ y \\end{array}\\!\\right) \\pi^{y} (1-\\pi)^{n-y} \\\\\n","& \\propto \\pi^{(\\alpha + y) - 1} (1-\\pi)^{(\\beta + n - y) - 1}  .\\\\\n","\\end{split}\n","$$\n","\n","3. 最后，我们加上归一化因子(分母部分)：\n","\n","$$\n","f(\\pi|y) = \\frac{\\Gamma(\\alpha+\\beta+n)}{\\Gamma(\\alpha+y)\\Gamma(\\beta+n-y)}\\pi^{(\\alpha + y) - 1} (1-\\pi)^{(\\beta + n - y) - 1}.\n","$$\n","\n","------------------\n","\n","我们知道$Beta(a,b)$的概率密度函数可以写为：\n","$$  \n","Beta(α, β) = \\frac{\\Gamma(\\alpha + \\beta)}{\\Gamma(\\alpha)\\Gamma(\\beta)} \\pi^{\\alpha-1} (1-\\pi)^{\\beta-1} \\;\\;  for\\; \\pi \\in [0,1] \\  \n","$$  \n","\n","因此，\n","\n","$$\n","\n","f(\\pi|y) = Beta(α + y, β + n − y)\n","\n","$$"]}],"metadata":{"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.11.3"}},"nbformat":4,"nbformat_minor":5}
